Improvement on the Calculation Method for Reflected Pressure of Shock Wave in Underwater Explosion

doi:10.12382/bgxb.2022.1037

Abstract

Abstract:

Gravity dam is a kind of common large concrete hydraulic construction. In order to explore a calculation method for the reflected pressure of shock wave applicable to the near area of hydraulic structure, a method for calculating the reflected pressure of shock wave of the underwater explosion on the rigid wall with clear physical connotation is derived strictly by using the three conservation basic relations of mass, momentum and energy on the shock wave front and the equation of state of condensed medium. Based on the relationship between shock wave velocity and particle velocity in continuous medium, the determination method of the state parameter k of water is given, and the law of state parameter k decaying exponentially with incident shock wave pressure is revealed. It is found that the change of k value has a significant impact on the calculation result of reflected pressure of shock wave when the incident pressure is above 725MPa. By comparing with the calculation methods proposed by Cole^[12], Henrych^[14], and Luo, et al^[15], and the numerical simulation, the results show that the proposed calculation method has a wider application scope and higher calculation accuracy, and it also reveals theoretically for the first time that the reflection pressure coefficient of underwater explosion shock wave ranges from 2.00 to 4.49.

Key words: underwater explosion, reflected pressure, rigid wall surface, Hugoniot relation, numerical simulation

CLC Number:

O382.1

YAN Zechen, YUE Songlin, QIU Yanyu, WANG Jianping, ZHAO Yuetang, SHI Jie, LI Xu. Improvement on the Calculation Method for Reflected Pressure of Shock Wave in Underwater Explosion[J]. Acta Armamentarii, 2024, 45(4): 1196-1207.

Figures/Tables 17

References 29

[1]	黄谢平, 孔祥振, 陈祖煜, 等. 近水面、库中、水下爆炸荷载作用下混凝土重力坝的破坏模式对比[J]. 土木工程学报, 2023, 56(3):116-128.
	HUANG X P, KONG X Z, CHEN Z Y, et al. Comparison of failure modes of concrete gravity dams by underwater explosion loads near the water free surface, the middle, and the bottom of the reservoir[J]. China Civil Engineering Journal, 2023, 56(3):116-128. (in Chinese)
[2]	FALCONER J. The dam busters story[M]. Sutton, LDN, UK: Sutton Publishing Ltd., 2007.
[3]	韦灼彬, 唐廷, 王立军. 港口水下爆炸荷载冲击特性研究[J]. 振动与冲击, 2014, 33(6): 18-22, 34.
	WEI Z B, TANG T, WANG L J. Shock characteristics of underwater explosion in port[J]. Journal of Vibration and Shock, 2014, 33(6):18-22, 34. (in Chinese)
[4]	WARDLAW A B, LUTON J A. Fluid-structure interaction mechanisms for close-in explosions[J]. Shock and Vibration, 2015, 7(5): 265-275.
[5]	梁浩哲, 张庆明, 杨莉. 刚性壁面附近深水爆炸气泡射流特性数值模拟[J]. 兵工学报, 2017, 38(增刊1): 130-135.
	LIANG H Z, ZHANG Q M, YANG L. Numerical investigation of jet characteristics of deepwater explosion bubbles near a rigid boundary[J]. Acta Armamentarii, 2017, 38(S1):130-135. (in Chinese)
[6]	刘靖晗, 唐廷, 韦灼彬, 等. 刚性柱附近浅水爆炸荷载特性研究[J]. 高压物理学报, 2019, 33(5): 166-173.
	LIU J H, TANG T, WEI Z B, et al. Pressure characteristics of shallow water explosion near the rigid column[J]. Chinese Journal of High Pressure Physics, 2019, 33(5): 166-173. (in Chinese)
[16]	LI W X. One-dimensional indeterminate flow and shock waves[M]. Beijing: National Defense Industry Press, 2003. (in Chinese)
[17]	HAAR L, GALLAGHER J S, KELL G S. NBC/NRC steam tables[M]. New York, NY, US: Hemisphere Publishing Corp, 1984.
[18]	汤文辉, 张若棋. 物态方程理论及计算概论[M]. 第2版. 北京: 高等教育出版社, 2008.
	TANG W H, ZHANG R Q. Introduction to theory and computation of equations of state[M]. 2nd ed. Beijing: Higher Education Press, 2008. (in Chinese)
[19]	宁建国, 王成, 马天宝. 爆炸与冲击动力学[M]. 北京: 国防工业出版社, 2010.
	NING J G, WANG C, MA T B. Explosion and shock dynamics[M]. Beijing: National Defense Industry Press, 2010. (in Chinese)
[20]	CHEREPANOV G P, ZAKIROV K R. State equation of condensed matter at high pressure: D-U diagram approach[J]. Physical Mesomechanics, 2014, 17(3): 163-177.
[21]	李维新. 凝聚介质的简化状态方程[J]. 爆炸与冲击, 1983, 3(2): 30-38.
	LI W X. A simplified equation of state in condensed medium[J]. Explosion and Shock Waves, 1983, 3(2): 30-38. (in Chinese)
[22]	SAITO T, MARUMOTO M, YAMASHITA H, et al. Experimental and numerical studies of underwater shock wave attenuation[J]. Shock Waves, 2003, 13(2): 139-148.
[23]	MARSH S P. LASL shock wave hugoniot data[M]. Berkeley and Los Angeles, CA, US: University of California Press, 1980.
[24]	邱清水, 陈莹玉, 古滨, 等. 水下近场爆炸载荷数值预报研究[J]. 四川轻化工大学学报(自然科学版), 2020, 33(5): 44-50.
[7]	刘靖晗, 韦灼彬, 唐廷, 等. 刚性壁或刚性单柱附近水下爆炸气泡脉动的数值研究[J]. 海军工程大学学报, 2020, 32(4): 106-112.
	LIU J H, WEI Z B, TANG T, et al. Numerical study on dynamic behavior of UNDEX bubble near rigid wall or rigid column[J]. Journal of Naval University of Engineering, 2020, 32(4): 106-112. (in Chinese)
[8]	李海涛, 朱石坚, 陈志坚, 等. 全入射角度下平板冲击波的壁压载荷及局部空化特性[J]. 爆炸与冲击, 2014, 34(3): 354-360.
	LI H T, ZHU S J, CHEN Z J, et al. Characteristics of wall pressure and cavitation on the plate subjected to underwater explosion shockwaves at any angle of incidence[J]. Explosion and Shock Waves, 2014, 34(3): 354-360. (in Chinese)
[9]	刘晓波, 李帅, 张阿漫. 水下爆炸冲击波壁压理论及数值计算方法改进研究[J]. 爆炸与冲击, 2022, 42(1): 123-135.
	LI X B, LI S, ZHANG A M. An improvement of the wall-pressure theory and numerical method for shock waves in underwater explosion[J]. Explosion and Shock Waves, 2022, 42(1): 123-135. (in Chinese)
[10]	闫秋实, 张志杰, 王丕光, 等. 水下爆炸荷载作用下圆柱结构反射压力解析计算方法研究[J]. 工程力学, 2022, 39(7): 247-256.
	YAN Q S, ZHANG Z J, WANG P G, et al. Research on analytical method of circular cylindrical scattered wave pressure subjected to underwater explosion[J]. Engineering Mechanics, 2022, 39(7): 247-256. (in Chinese)
[11]	毛致远, 段超伟, 宋浦, 等. 基于有效冲量的水下爆炸冲击波对平板结构的毁伤准则[J]. 高压物理学报, 2023, 37(2): 025103.
	MAO Z Y, DUAN C W, SONG P, et al. Criterion of plate structure damage caused by underwater explosion shock wave based on effective impulse[J]. Chinese Journal of High Pressure Physics, 2023, 37(2): 025103. (in Chinese)
[12]	COLE R H. Underwater explosions[M]. Princeton, NJ, US: Princeton University Press, 1948.
[13]	罗兴柏, 张玉令, 丁玉奎. 爆炸力学理论教程[M]. 北京: 国防工业出版社, 2016.
	LUO X B, ZHANG Y L, DING Y K. A course in the theory of explosive mechanics[M]. Beijing: National Defense Industry Press, 2016. (in Chinese)
[14]	HENRYCH J. The dynamics of explosion and its use[M]. New York, NY, US: Elsevier Scientific Publishing Company, 1979.
[15]	罗泽立, 周章涛, 毛海斌, 等. 水下爆炸强冲击波与平板结构相互作用的理论分析方法[J]. 高压物理学报, 2017, 31(4): 443-452.
	LUO Z L, ZHOU Z T, MAO H B, et al. Theoretical analysis of the interaction between the plate structure and strong shock wave in underwater explosion[J]. Chinese Journal of High Pressure Physics, 2017, 31(4): 443-452. (in Chinese)
[16]	李维新. 一维不定常流与冲击波[M]. 北京: 国防工业出版社, 2003.
[24]	QIU Q S, CHEN Y Y, GU B, et al. Numerical prediction of underwater near field explosion load[J]. Journal of Sichuan University of Science& Engineering( Natural Science Edition), 2020, 33(5): 44-50. (in Chinese)
[25]	WANG G H, WANG Y X, LU W B, et al. On the determination of the mesh size for numerical simulations of shock wave propagation in near field underwater explosion[J]. Applied Ocean Research, 2016, 59: 1-9.
[26]	李晓杰, 张程娇, 王小红, 等. 水的状态方程对水下爆炸影响的研究[J]. 工程力学, 2014, 31(8): 46-52.
	LI X J, ZHANG C J, WANG X H, et al. Numerical study on the effect of equations of state of water on underwater explosions[J]. Engineering Mechanics, 2014, 31(8): 46-52. (in Chinese)
[27]	ZAMYSHLYAEV B V, YAKOVLEV Y S. Dynamic loads in underwater explosion[M]. Washington, D C, US: Naval Intelligence Support Center, 1973.
[28]	宫翔飞, 刘文韬, 张树道, 等. 水下爆炸近场峰值压力的数值模拟[J]. 爆炸与冲击, 2019, 39(4): 041409.
	GONG X F, LIU W T, ZHANG S D, et al. Numerical simulation of peak pressure in near-field underwater explosion[J]. Explosion and Shock Waves, 2019, 39(4): 041409. (in Chinese)
[29]	赵文达, 赵玉红, 闫秋实. 水下爆炸荷载作用下重力式沉箱码头破坏效应研究[C]// 第28届全国结构工程学术会议论文集(第2册). 南昌: 工程力学编辑部, 2019: 496-505.
	ZHAO W D, ZHAO Y H, YAN Q S. Study on destructive effect of gravity caisson wharf under underwater explosion[C]// Proceedings of the 28th National Conference on Structrual Engineering(No.Ⅱ). Nanchang: Editorial Department of Engineering Mechanics, 2019: 496-505. (in Chinese)

T/℃	ρ₀/(g·cm^-2)	c₀/(km·s^-1)
5	1.0000	1.426
10	0.9997	1.448
20	0.9980	1.483
40	0.9920	1.528
60	0.9830	1.549
80	0.9720	1.553
90	0.9650	1.549

T/℃	ρ₀/(g·cm^-2)	c₀/(km·s^-1)
5	1.0000	1.426
10	0.9997	1.448
20	0.9980	1.483
40	0.9920	1.528
60	0.9830	1.549
80	0.9720	1.553
90	0.9650	1.549

序号	p/GPa	计算结果	拟合结果	误差/%
1	0.05	6.82	6.76	-0.88
2	0.10	6.67	6.66	-0.15
3	0.20	6.41	6.46	0.78
4	0.50	5.90	5.97	1.19
5	1.00	5.41	5.40	-0.18
6	2.00	4.87	4.79	-1.64
7	5.00	4.17	4.18	0.24
8	10.00	3.66	3.73	1.91
9	15.00	3.37	3.39	0.59
10	20.00	3.16	3.14	-0.63
11	25.00	2.99	2.95	-1.34
12	30.00	2.84	2.80	-1.41
13	35.00	2.71	2.69	-0.74
14	40.00	2.60	2.61	0.38
15	45.00	2.49	2.54	2.01

序号	p/GPa	计算结果	拟合结果	误差/%
1	0.05	6.82	6.76	-0.88
2	0.10	6.67	6.66	-0.15
3	0.20	6.41	6.46	0.78
4	0.50	5.90	5.97	1.19
5	1.00	5.41	5.40	-0.18
6	2.00	4.87	4.79	-1.64
7	5.00	4.17	4.18	0.24
8	10.00	3.66	3.73	1.91
9	15.00	3.37	3.39	0.59
10	20.00	3.16	3.14	-0.63
11	25.00	2.99	2.95	-1.34
12	30.00	2.84	2.80	-1.41
13	35.00	2.71	2.69	-0.74
14	40.00	2.60	2.61	0.38
15	45.00	2.49	2.54	2.01

序号	p_i/ MPa	本文方法p_r/ MPa	Cole^[12]方法		罗兴柏等^[13]方法		Henrych^[14]方法		罗泽立等^[15]方法
序号	p_i/ MPa	本文方法p_r/ MPa	p_r/MPa	偏差/%	p_r/MPa	偏差/%	p_r/MPa	偏差/%	p_r/MPa	偏差/%
1	50	104.15	104.28	-0.13	104.14	0.01	102.98	1.13	102.88	1.23
2	100	215.45	216.71	-0.58	216.23	-0.36	212.25	1.51	211.14	2.04
3	200	454.43	460.74	-1.37	459.17	-1.03	447.33	1.59	441.67	2.89
4	500	1253.48	1300.20	-3.59	1293.94	-3.13	1260.03	-0.52	1218.21	2.89
5	1000	2728.15	2921.05	-6.60	2905.65	-6.11	2861.58	-4.66	2687.19	1.52
6	2500	7613.65	8642.45	-11.90	8206.75	-7.23	8550.53	-10.96	7621.90	-0.11
7	5000	16381.42	19648.15	-16.63	18776.65	-12.76	19057.31	-14.04	16359.08	0.14
8	7500	25514.07	31709.14	-19.54	30451.77	-16.21	29959.43	-14.84	25266.46	0.98
9	10000	34927.55	44482.23	-21.48	42880.84	-18.55	41007.72	-14.83	34231.58	2.03
10	25000	96476.96	129874.11	-25.72	126832.20	-23.93	108084.80	-10.74	88314.55	9.24
11	35000	141132.22	192007.84	-26.50	188432.98	-25.10	152993.88	-7.75	124437.63	13.42
12	45000	187223.67	256913.84	-27.13	253060.19	-26.02	197941.73	-5.41	160573.99	16.60